See capacitors C1 and C2. C1 is several microfarads and C2 is 100 nF. These are the bypass capacitors on the power supply.
The TM1637 datasheet specifies the option of capacitors C3 and C4 to suppress transients on the two data lines.
100pF capacitor connected to the DIO, CLK communication port pull-up and pull-down can reduce interference to radio communications port
Note the value specified is 100 picofarads.
Well, the bright sparks who assembled these boards didn't feel like inventorying 100 pF capacitors, so they just used 100 nF - nanofarad to match C2. The value is therefore one thousand times the specified value and prevents the transfer of the data unless you ran the software very, very slowly (presumably, 1000 times slower ).
I would expect ESP8266 to work fine with TM1637 (with VCC = 3.3V)
However, ESP8266 has no reliable Arduino pin-mapping. When you say CLK=9 do you know which ESP8266 GPIO pin you have actually connected?
I use the Uno-format D1 R1 board. It has Uno headers but you use D9 and not 9 for digital#9 header pin.
David.
Edit. Selected "Wemos R1 D1" as ESP8266 board. Edited the TM1637Test.ino example from the TM1637Display.h library installed from the IDE Library Manager.